mentat@walt.cc.utexas.edu (Robert Dorsett) (09/15/89)
I'm looking for references to algorithms that can take two coordinates on a sphere, and produce a set of points that describe the shortest path between those two points. The closer these algorithms come to carto- graphic techniques of plotting great circle tracks in a two-dimensional space, the better. Please respond by email; I'll summarize in a week or so. Robert Dorsett Internet: rdd@rascal.ics.utexas.edu UUCP: ...cs.utexas.edu!rascal.ics.utexas.edu!rdd
hallett@pet3.uucp (Jeff Hallett x5163 ) (09/15/89)
In article <18393@ut-emx.UUCP> mentat@walt.cc.utexas.edu (Robert Dorsett) writes: > >I'm looking for references to algorithms that can take two coordinates >on a sphere, and produce a set of points that describe the shortest path >between those two points. The closer these algorithms come to carto- >graphic techniques of plotting great circle tracks in a two-dimensional >space, the better. You are basically looking for the geodesic between the two points and then taking the shortest connective segment of the geodesic. Any book on differential geometry will have the solution for you (I don't have it with me). Another method would be to determine the plane defined by the two points and the sphere center. Find the intersection of the sphere with that plane, a circle in the plane. The shorter segment of that circle bounded by the two points is the track you seek. (Of course, these are really the same methods. However, determining the true geodesic would then simply extend the problem to any differentiable manifold.) -- Jeffrey A. Hallett, PET Software Engineering GE Medical Systems, W641, PO Box 414 Milwaukee, WI 53201 (414) 548-5163 : EMAIL - hallett@positron.med.ge.com